Optimal Type-2 Fuzzy Controller For HVAC Systems

Mohammad Hassan Khooban, Davood Nazari Maryam Abadi, Alireza Alfi, Mehdi Siahi

Optimal Type-2 Fuzzy Controller For HVAC Systems

DOIUDKIFAC

10.7305/automatika.2014.01.219681.515.8.017-53:[697+644]2.2; 5.5.1.5

Original scientific paper

In this paper a novel Optimal Type-2 Fuzzy Proportional-Integral-Derivative Controller (OT2FPIDC) is designedfor controlling the air supply pressure of Heating, Ventilation and Air-Conditioning (HVAC) system. The param-eters of input and output membership functions, and PID controller coefficients are optimized simultaneously byrandom inertia weight Particle Swarm Optimization (RNW-PSO). Simulation results show the superiority of theproposed controller than similar non-optimal fuzzy controller.

Key words: HVAC systems, Optimal Type-2 Fuzzy Proportional-Integral-Derivative controller (OT2FPIDC),Random inertia weight particle swarm optimization (RNW-PSO)

Optimalni neizraziti reglutor tipa 2 za sustave za grijanje, ventilaciju i klimatizaciju. U radu je pred-ložena nova upravljacka shema optimalnog neizrazitog PID regulatora tipa 2 za upravljanje sustavima za grijajne,ventilaciju i klimatizaciju. Predložena je shema zasnovana na neizrazitom regulatoru (FLC) ucestalo korištenomza upravljajne nelinearnim procesima. Kako bi se premostio problem neizrazitih regulatora, neodstatak metodedizajnirajna, parametri ulazno-izlaznih funkcija pripadanja, kao i parametri PID regulatora se optimiraju metodomroja cestica sa slucajnim parametrima inercije (RNW-PSO). Simulacijski rezultati pokazuju izvedivost predloženogpristupa.

Kljucne rijeci: HVAC sustavi, neizrazitog PID regulatora tipa 2 za upravljanje sustavima (OT2FPIDC), algoritamroja cestica sa slucajnim parametrima inercije (RNW-PSO)

1 INTRODUCTION

Heating, Ventilation and Air-Conditioning (HVAC)mechanisms are needed for setting environmental vari-ables including, temperature, moisture, and pressure. Aswith other industrial usages, most of the processes asso-ciated with HVAC are controlled by PID controllers. Theprevalent PID controllers are extensively applied becauseof their easy calculations, easy application, appropriate ro-bustness, high dependability, stabilizing and zero persis-tent state error. However HVAC mechanism is a non-linear and time variant mechanism. It is hard to accessfavorable tracking control efficiency, because tuning andself-adapting adjustment of parameters automatically area perennial issue of PID controller. During the recentdecades various methods for identifying PID controller pa-rameters have been presented. In some techniques the openloop response information of system is used, for instanceCohen-Coon reaction curve procedure [1].

In recent years, researchers have extensively used thefuzzy logic for modeling, identification, and control ofhighly nonlinear dynamic systems [2,3]. In [4-8], different

combination of control methods are suggested to improvethe efficiency of fuzzy PI or PID controllers. Adjustmentprocess of PID controller coefficients can take a long time,and can be hard and costly work [8,9]. Usually a proficientgainer attempts to control the process by adjusting the co-efficients of controller according to error and change rateof error in order to achieve the optimal response. In thispaper the optimal adjustment is obtained by random iner-tia weight Particle Swarm Optimization (RNW-PSO).

In the HVAC mechanism the supply air pressure istuned by changing the speed of a supply air fan. The rela-tionship between fan speed and pressure of air source canbe expressed by a delayed second order transfer functionas is described by Bi and Cai [11]. Since in various operat-ing conditions both fans and dampers show non-linear be-haviour from themselves, even a well-regulated controlleris unable to meet design requirements due to the existinguncertainties in parameters of system.

Motivated by the aforementioned researches, thepurpose of this paper is to present a novel OptimalType-2 Fuzzy Proportional Integral Derivative Controller(OT2FPIDC) for regulating the air supply pressure of

Online ISSN 1848-3380, Print ISSN 0005-1144ATKAFF 55(1), 69–78(2014)

AUTOMATIKA 55(2014) 1, 69–78 69

Optimal Type-2 Fuzzy Controller For HVAC Systems M. H. Khooban, D. N. M. Abadi, A. Alfi, M. Siahi

Fig. 1. An IT2 FLS

Heating, Ventilation and Air-Conditioning (HVAC) sys-tem. The parameters of input and output membership func-tions, and PID controller coefficients are optimized simul-taneously by random inertia weight Particle Swarm Opti-mization (RNW-PSO). Simulation results indicate that theproposed controller has faster response, smaller overshootand higher accuracy than Proportional Integral Deriva-tive PID, Adaptive Neuro Fuzzy (ANF), and Self-TuningFuzzy PI Controlle (STFPIC) under normal condition andunder existing uncertainties in parameters of model.

2 TYPE-2 FUZZY SETS AND SYSTEMS

Type-2 fuzzy sets and systems generalize (type-1)fuzzy sets and systems so that more uncertainty can behandled. From the very beginning of fuzzy sets, criticismwas made about the fact that the membership function ofa type-1 fuzzy set has no uncertainty associated with it,something that seems to contradict the word fuzzy, sincethat word has the connotation of lots of uncertainty.

2.1 Interval Type 2 Fuzzy Sets (IT2 FSs)

In spite of having a name which carries the concept ofuncertainty, studies has demonstrated that there are restric-tions in the ability of T1 FSs to model and minimize theeffect of uncertainties [12-15]. This is because a T1 FSis fixed this means that its membership degrees are crispamounts. Lately, type-2 FSs [16], specified by MFs thatare themselves fuzzy, have been attracting interests. Inter-val type-2 (IT2) FSs [14], a special case of type-2 FSs, arecurrently the most widely used for their reduced computa-tional cost.

2.2 Interval Type-2 Fuzzy Logic System (IT2 FLS)

Fig. 1 indicates the schematic diagram of an IT2 FLS.It is similar to its T1 equivalent, the main difference beingthat at least one of the FSs in the rule base is an IT2 FS.Hence, the outputs of the inference engine are IT2 FSs,and a type-reducer is required to convert them into a T1 FSbefore defuzzification can be performed.

Actually the calculations in an IT2 FLS can be con-siderably simplified. Consider the rulebase of an IT2 FLS

consisting of N rules, supposing the following form:

Rn : IF x1 is Xn1 ...and x1 is X

n1 . THENy is Y

n,n=1,2,...,N,

where Xni (i = 1, . . ., I) are IT2 FSs, and Yn = [yn, yn]

is an interval, which can be understood as the centroid [13,16] of a consequent IT2 FS, or the simplest TSK model,for its simplicity. In many applications we use yn = yn ,i.e., each rule consequent is a crisp number. Suppose theinput vector is x′ = (x′1, x

′2, . . . , x

′I). Typical calculations

in an IT2 FLS include the following steps:

1. Calculate the membership of x′i on each Xni ,

[µXni (x′i), µX

n

i (x′i)], i = 1, 2, . . . , I, n = 1, 2, . . . ,N.(1)

2. Calculate the firing interval of the nth rule, Fn(x):

Fn(x′) = [µXn1 (x′1)× ... × µXn

1 (x′1), µXn1 (x′1)×

... × µXn1 (x′1)] ≡ [fn, fn], n = 1, ... , N

(2)

3. Apply type-reduction to combine Fn(x′) and the re-lated rule consequents. There are many such meth-ods. The most commonly used one is the center-of-sets type-reducer [13]:

Ycos(x′) =

⋃

fn ∈ Fn(x′)yn ∈ Y n

∑Nn=1 f

nyn∑Nn f

n= [yl, yr]

(3)

It has been demonstrated that [14,18,19]:

yl = mink∈[1,N−1]

∑kn=1 f

nyn +∑Nn=k+1 f

nyn

∑kn=1 f

n +∑Nn=k+1 f

n

=

∑Ln=1 f

nyn +∑Nn=L+1 f

nyn

∑Ln=1 f

n +∑Nn=L+1 f

n

yl = maxk∈[1,N−1]

∑kn=1 f

nyn +∑Nn=k+1 f

nyn

∑kn=1 f

n +∑Nn=k+1 f

n(4)

=

∑Rn=1 f

nyn +∑Nn=R+1 f

nyn

∑Rn=1 f

n +∑Nn=R+1 f

n(5)

, where the switch points L and R are specified by

yL ≤ yl ≤ yL+1 (6)

70 AUTOMATIKA 55(2014) 1, 69–78


yR ≤ yr ≤ yR+1 (7)

and yn and yn have been sorted in ascending order, re-spectively. yl and yr can be calculated using the Karnik-Mendel (KM) algorithms [14].

KM Algorithm for Computing yl [20]:

1. Sort yn

(n = 1, 2, . . . , N ) in increasing order andcall the sorted y

nby the same name, but now y

1=

y2· · · = y

N. Match the weights Fn(x′) with their

respective yn

and renumber them so that their indexcorresponds to the renumbered y

n.

2. Initialize fn by setting

fn =fn + fn

2n = 1, 2, ..., N (8)

and then compute

y =

∑Nn=1 f

nyn

∑Nn f

n(9)

3. Find switch point k (1 k N – 1) such that

yk ≤ y ≤ yK+1 (10)

4. Setfn = {f

n, n≤kfn , n�k (11)

And calculate

y′ =

∑Nn=1 f

nyn

∑Nn f

n(12)

5. Check if y′ = y. If yes, stop and set yr = y andL = k. If no, go to Step 6.

6. Set y′ = y and go to Step 3.

KM Algorithm for Computing yr [20]:

1. Sort yn(n = 1, 2, . . . , N) in increasing order andcall the sorted yn by the same name, but now y1 =y2 . . . yN . Match the weights Fn(x′) with their re-spective yn and renumber them so that their index cor-responds to the renumbered yn.

2. Initialize fn by setting

fn =fn + fn

2n = 1, 2, ..., N

and then calculate

y =

∑Nn=1 f

nyn∑Nn f

n(13)

3. Find switch point k (1 k N – 1) such that

yk ≤ y ≤ yK+1 (14)

4. Set

fn = {fn, n≤kfn , n�k (15)

and calculate

y′ =

∑Nn=1 f

nyn∑Nn f

n(16)

5. Check if y′ = y. If yes, stop and set yr = y and R =k. If no, go to Step 6.

6. Set y′ = y and go to Step 3.

The main idea of the KM algorithm is to find theswitch points for yl and yr.

7. Compute the defuzzified output as:

y =yl + yr

2(17)

3 PARTICLE SWARM OPTIMIZATIONThe PSO algorithm is a partly new population-

based heuristic optimization method which is based on ametaphor of social interaction, specifically bird flocking.The main benefits of PSO are: 1) The cost function’s gra-dient is not needed, 2) PSO is more compatible and robustcompared with other classical optimization techniques, 3)PSO guarantees the convergence to the optimum solution,and 4) In comparison with GA, PSO lasts fewer time foreach function evaluation as it does not apply many of GAoperators such as mutation, crossover and selection opera-tor.

In PSO, any nominee solution is named “Particle”.Each particle in the swarm demonstrates a nominee so-lution to the optimization problem, and if the solution iscomposed of a series of variables, the particle can be a vec-tor of variables. In PSO, each particle is flown through themultidimensional search space, regulating its position insearch space based on their momentum and both personaland global histories. Then the particle uses the best posi-tion faced by itself and that of its neighborhood to positionitself toward an optimal solution. The appropriateness ofeach particle can be assessed based on the cost functionof optimization problem. At each repetition, the speed ofevery particle will be computed as follows:

vi(t+1) = ωvi(t)+c1rq(Pid−xi(t))+c2r2 (Pgd − xi(t)) ,(18)

AUTOMATIKA 55(2014) 1, 69–78 71


where xi(t) is the present position of the particle, pid is oneof the finest solutions this particle has achieved and pgd isone of the finest solutions all the particles have achieved.After computing the speed, the new position of each parti-cle will be computed as follows

xi(t+ 1) = xi(t) + vi(t+ 1). (19)

The PSO algorithm is replicated using Eqs. 18 and 19which are updated at each repetition, up to pre-definednumber of generations is achieved.

3.1 Random inertia weight PSOAlthough Standard PSO (SPSO) includes some signif-

icant improvements by providing high rate of convergencein particular problems, it does demonstrate some deficien-cies. It is shown that SPSO has a weak capability to lookfor a fine particle due to the lack of speed control mecha-nism. Most of the procedures are tried to ameliorate the ef-ficiency of SPSO by changeable inertia weight. The inertiaweight is essential for the efficiency of PSO, which equili-brates global exploration and local exploitation capabilitiesof the swarm. A large inertia weight simplifies exploration,but it prolongs the convergence of particle. Unlike, a smallinertia weight leads to rapid convergence, but it sometimesresults local optimum. Therefore different inertia weightconformity algorithms have been recommended in the lit-eratures [21]. In 2003 Zhang [22] studied the effect of ran-dom inertia weight in PSO (RNW-PSO), reporting empir-ical results that show its superior efficiency to LDW-PSO[23]. Eberhart and Shi [24] have recommended a randominertia weight factor for tracking dynamic systems. Thenew version of PSO namely RNW-PSO can be obtainedby changing Eq. ((18)) as below

vi(t+1) = r0vi(t)+c1r1(Pid−xi(t))+c2r2 (Pgd − xi(t)) ,(20)

where r0 is a uniformly distributed random number insidethe interval [0, 1], and other parameters are same as be-fore. The RNW can overcome two bugs of LDW. First,decreasing the affiliation of inertial weight on the maxi-mum repetition that is hardly predicted before tests. Sec-ond, abstaining from the lacks of local search capabilityin the beginning of run and global search capability at theend of run. Before starting the optimization procedure, aperformance benchmark should be first presented.

3.2 Empirical StudiesIn order to examine the effect of inertia weight on the

PSO efficiency, three non-linear benchmark functions pre-sented in literature [25, 26] were used because they are fa-mous problems. The first function is the Rosenbrok func-tion:

Table 1. Vmax and Xmax values used for testsFunction Xmax Vmax

f1 100 100f2 10 10f3 600 600

f1(x) =

n∑

i=1

(100(xi+1 − x2i )

2 + (xi − 1)2), (21)

where x = [x1, x2, . . . , xn] is an n-dimensional real-valued vector.

The second is the generalized Rastrigrin function:

f2(x) =

n∑

i=1

(x2i − 10 cos(2πxi) + 10). (22)

The third is the generalized Griewank function:

f3(x) =1

4000

n∑

i=1

x2i −

n∏

i=1

cos(xi√i) + 1. (23)

Three various amounts dimensions were tested: 10, 20and 30. The maximum numbers of repetition were set as1000, 1500 and 2000 in accordance with the dimentions10, 20 and 30, respectively. For evaluation the scalabil-ity of PSO algorithm, three population sizes 20, 40 and 80were used for each function according to various dimen-sions. Acceleration constants took the values c1 = c2 = 2.Constriction factor C = 1. To perform comparison, allthe Vmax and Xmax were assigned by same parameter set-tings as in literature [26] and mentioned in Table 1. 500trial runs were taken for each case

4 THE PROPOSED CONTROL METHOD

General scheme of proposed controller is shown inFig. 2. The two inputs of the controller are the error e andthe change rate of error e , respectively and the output ofcontroller is U. The main shortage of the optimal Type-2fuzzy-PID controller is the lack of systematic approachesto define fuzzy rules and fuzzy membership functions. Aswe know, most fuzzy rules are based on human knowledgeand differ among persons despite the same system perfor-mance. Because of this, it is complex to assume that thegiven expert’s knowledge captured in the form of the fuzzycontroller leads to optimal control. Therefore, the efficientapproaches for tuning the membership function and controlrules without a trial and error method are significantly re-quired. Because of this, the idea of employing RNW-PSOalgorithm to achieve best rising time (tr), settling time (ts),

72 AUTOMATIKA 55(2014) 1, 69–78


Table 2. The used parameters of RNW-PSOSize of the Swarm 50Dimension of Problem 20Maximum Number of iterations 100Cognitive Parameter C1 1Social Parameter C2 1Construction Factor C 1

Fig. 2. Optimal Type-2 Fuzzy-PID controller

% peak overshoot (Mp), steady-state error (Ess) is repre-sented [28]. Generally, the heuristic algorithm like PSOonly requires to check the cost function for guidance of itssearch and no longer requiring informations about the sys-tem. So, in this paper, the Least Mean Square (LMS) oferror is considered. The parameters of RNW-PSO are alsolisted in Table 2.

In the use of Gaussian membership functions we willface with three different cases. 1) Gaussian membershipfunctions with the same means and variances, 2) Gaussianmembership functions with the same means and variablevariances, and 3) Gaussian membership functions withvariable means and the same variances. In [28] an optimalfuzzy-PI controller is designed for a nonlinear delay differ-ential model of glucose-insulin regulation system, and it isshown that Gaussian membership functions with variablemeans and the same variances have better performance incontrolling this system, therefore we applied this idea indesign process with the difference that the variances areselected interval.

The specifications of the input and output variables aregiven in Tables 3 and 4, respectively.

The rulebase has the following nine rules:

• R1 : IF e is E-N and e is CE-N , THEN U is NL.

• R2 : IF e is E-N and e is CE-Z, THEN U is NS.

• R3 : IF e is E-N and e is CE-P , THEN U is Z.

• R4 : IF e is E-Z and e is CE-N , THEN U is NS.

Table 3. The Parameters of Input Gaussian MembershipFunctions

InputVariables

MembershipFunctions

Mean VarianceInterval

Negative(E − N)

−0.0751 [0.07910.1881]

Eror (E) Zero(E − Z)

0.0527 [0.07910.1881]

Positive(E − P )

7.7634× 10−4 [0.07910.1881]

Negative(CE − N)

−0.1612 [0.00700.0231]

Change ofError (CE)

Zero(CE − Z)

0.0311 [0.00700.0231]

Positive(CE − P )

0.0215 [0.00700.0231]

Table 4. The Parameters of Output Gaussian MembershipFunctions

OutputVariables

MembershipFunctions

Mean VarianceInterval

Negative Large(NL)

−0.0141 [0.01220.0486]

Negative Small(NS)

−0.1051 [0.01220.0486]

ControlInput (U)

Zero (Z) −0.1681 [0.01220.0486]

Positive Small(PS)

0.0549 [0.01220.0486]

Positive Large(PL)

0.3496 [0.01220.0486]

• R5 : IF e is E-Z and e is CE-Z, THEN U is Z.

• R6: IF e is E-Z and e is CE-P , THEN U is PS.

• R7 : IF e is E-P and e is CE-N , THEN U is Z.

• R8 : IF e is E-P and e is CE-Z, THEN U is PS.

• R9 : IF e is E-P and e is CE-P , THEN U is PL.

The firing intervals and consequents of the nine rulesgiven in Table 5.

From the KM algorithms,yl and yr can be computed asfollow:

yl =f

1NL

1+ f 2NS

2+ f3Z

3+ f 4NS

4

f1

+ f2 + f3 + f4+f5 + f6 + f7 +f8 + f9

+f5Z

5+ f 6PS

6+ f7Z

7+ f 8PS

8+ f 9PL

9

f1

+ f2 + f3 + f4+f5 + f6 + f7 +f8 + f9

AUTOMATIKA 55(2014) 1, 69–78 73


Table 5. Firing intervals of the nine rulesRuleNo.:

Firing Interval Consequent

R1 [f1, f1] = [µE−N (e)× µCE−N (e)

, µE−N (e)× µE−N (e)]

[NL1, NL1]

R2 [f2, f2] = [µE−N (e) × µCE−Z(e)

, µE−N (e)× µCE−Z(e)]

[NS2, NS2]

R3 [f3, f3] = [µE−N (e) µCE−P (e) ,

µE−N (e)× µCE−P (e)]

[Z3, Z3]

R4 [f4, f4] = [µE−Z(e) × µCE−N (e)

, µE−Z(e)× µCE−N (e)]

[NS4, NS4]

R5 [f5, f5] = [µE−Z(e)× µCE−Z(e) ,

µE−Z(e)× µCE−Z(e)]

[Z5, Z5]

R6 [f6, f6] = [µE−Z(e) × µCE−P (e)

, µE−Z(e)× µCE−P (e)]

[PS6, PS6]

R7 [f7, f7] = [µE−P (e) × µCE−N (e)

, µE−P (e)× µCE−N (e)]

[Z7, Z7]

R8 [f8, f8] = [µE−P (e) × µCE−Z(e)

, µE−P (e)× µCE−Z(e)]

[PS8, PS8]

R9 [f9, f9] = [µE−P (e) × µCE−P (e)

, µE−P (e)× µCE−P (e)]

[PL9, PL9]

yr =f1NL

1

+ f2NS2

+ f3Z3

+ f4NS4

f1 + f2 + f3 + f4 + f5 + f6 + f7 + f8 + f9

+f5Z

5+ f6PS

6

+ f7Z7

+ f8PS8

+ f9PL

9

f1 + f2 + f3 + f4 + f5 + f6 + f7 + f8 + f9

Finally, the crisp output of the IT2 FLS, y, can be cal-culated as follow:

y =yl + yr

2. (24)

5 SIMULATIONS AND RESULTS

In order to simulate the proposed controller, MATLABsoftware is applied. The simulation is run on a personalcomputer Core 2 Due, 2.8 GHz, 4 Gbytes RAM, underWindows 7. The RNW-PSO optimizes the controller’sparameters dynamically. To minimize fitness function,in each iteration, the parameters are randomly chosen byRNW-PSO algorithm. These parameters consist of meanand variance of Gaussian membership functions and PIDcontroller’s coefficients. Then the program will be run. Inthe end of run, the fitness function’s value is calculatedand is compared with the value calculated in previous it-erations. If the new value be better than previous values,the new estimated values for parameters are stored. Aftercompletion of iteration loop, RNW-PSO algorithm offersthe best answer as an optimal answer. The optimal param-eters of PID controller are given in Table 6. The transfer

Table 6. Optimal parameters of PID controllerProportional Gain - Kp 1.1814Derivative Gain - Kd 0.0473

Integral Gain - Ki 1.5056

Fig. 3. Obtained membership functions of input 1

function of the supply air pressure loop under normal cir-cumstances is as follows:

G(s) =0.81e−2s

(0.97s+ 1)(0.1s+ 1), (25)

where gain K = 0.81, τ1 = 0.97, τ2 = 0.1 and deadtime δ = 2 sec. For this process weighting parameters aredefined Ne = 0.9, Ne = 5 and Nu = 2.5. Input andoutput membership functions of designed optimal type-2fuzzy-PID controller namely error (Input 1), change of er-ror (Input 2), and control input are shown in Figs. 3, 4, and5 respectively. It can be observed from these Figs that theRNW-PSO has improved the logical sequence of member-ship functions. For instance, about input 2 the membershipfunction CE-P comes before CE-Z.

In order to evaluate controller performance againstthe existing uncertainties in parameters of nominal modelthree different transfer function has been introduced. Toinvestigate this issue the applied transfer functions in [29]is used.

1. when gain K = 0.81, τ1 = 0.2, τ2 = 2 and dead time

Fig. 4. Obtained membership functions of input 2

74 AUTOMATIKA 55(2014) 1, 69–78


Fig. 5. Obtained membership functions of Output

δ = 2 sec., then the transfer function of the supply airpressure loop is as follow

G(s) =0.81e−2s

(0.97s+ 1)(0.1s+ 1)(26)

For this process weighting parameters are definedNe = 0.9, Ne = 15 and Nu = 0.3.

2. when gain K = 1.2, τ1 = 0.97, τ2 = 0.1 and deadtime δ = 3 sec., then the transfer function of the sup-ply air pressure loop is as follow

G(s) =1.2e−3s

(0.97s+ 1)(0.1s+ 1)(27)

For this process weighting parameters are definedNe = 0.9, Ne = 3 and Nu = 1.

3. when gain K = 1.2, τ1 = 0.97, τ2 = 0.1 and deadtime δ = 4 sec., then the transfer function of the sup-ply air pressure loop is as follow

G(s) =1.2e−4s

(0.97s+ 1)(0.1s+ 1)(28)

For this process weighting parameters are definedNe = 0.9, Ne = 3 and Nu = 1.

The Figs. 6-9 and Table 7 are indicated that the supplyair pressure loop of HVAC acts satisfactorily both undernominal transfer function and also under existing uncer-tainties in parameters of model. Table 8 implies that boththe rise time and settling time are highly appropriate. Peakovershoots are also demonstrated insignificant when Opti-mal Type-2 Fuzzy-PID Controller (OT2FPIDC) is applied.The proposed controller in this paper is much less com-plicated than the existing non-optimal fuzzy controller in[30]. The designed controller in this paper has only 9 ruleswhereas with these limited rules the design requirementsare satisfied. But in [30] for achieving the satisfactory re-sults 49 rules are defined. This fact shows the superiorityof the controller in this paper than the controller proposedin [30].

Fig. 6. Performance of the transfer function given byEq. (25)



AUTOMATIKA 55(2014) 1, 69–78 75



Table 7. Performance analysis of OT2FPIDC for differentHVAC-Supply Air Pressure Loop

Transfer function tr sec ts sec Mp% Ess%G(s)= 0.81e−2s

(0.97s+1)(0.1s+1)2.58 4.74 0.00 0.12

G(s)= 0.81e−2s

(0.2s+1)(2s+1)4.44 8.17 0.00 0.01

G(s)= 1.2e−3s

(0.97s+1)(0.1s+1)2.16 5.88 0.00 0.08

G(s)= 1.2e−4s

(0.97s+1)(0.1s+1)2.26 6.75 0.00 0.06

Table 8. Comparison between performance of PID, ANF,STFPIC, and OT2FPIDC under normal condition and un-der existing uncertainties in parameters of model

Transfer Function ControllerType

Mp % ts sec

G(s)= 0.81e−2s

(0.97s+1)(0.1s+1)

PID 3.9 6.7ANF 3.5 7.5STFPIC 0.00 3.6OT2FPIDC 0.00 4.74

G(s)= 0.81e−2s

(0.2s+1)(2s+1)

PID 17.9 16.2ANF 0.9 10.6STFPIC 0.088 8.9OT2FPIDC 0.00 8.17

G(s)= 1.2e−3s

(0.97s+1)(0.1s+1)

PID 63 37ANF 56 19STFPIC 17.6 6OT2FPIDC 0.00 5.88

G(s)= 1.2e−4s

(0.97s+1)(0.1s+1)

PID 100 ≥ 120ANF 59 32STFPIC 25 6.9OT2FPIDC 0.00 6.75

6 CONCLUSION

A novel optimal type-2 fuzzy-PID controller has beensuggested for temperature regulation of HCAC system.Simulation results indicate that the new optimal fuzzy-PID controller has faster response, smaller overshoot andhigher accuracy than PID, ANF, and STFPIC under normalcondition and under existing uncertainties in parameters ofmodel. The new optimal type-2 fuzzy-PID controller canbe extensively applied in the HVAC industry.

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Mohammad Hassan Khooban received theB.Sc. degree in Control Engineering from theFars Science and Research Branch, in 2010 andM.Sc. degrees in Control Engineering from Is-lamic Azad University, Iran, in 2012. His em-ployment experience included working at Sar-vestan Branch-Islamic Azad University of Iran,Advisor to Iranian Space Agency, Iranian SpaceCenter, Mechanic Institute, Shiraz, Iran, sincenow. His research interests include HeuristicOptimization, Nonlinar Robust Control, Fuzzy

Logic and Power Systems.

Davood Nazari Maryam Abadi received theB.Sc, in Elec. Eng. from the Sadjad Instituteof Higher Education Mashhad, Iran. He receivedthe M.Sc, in Elec. Eng. from the Azad Universityof Iran, Garmsar branch, Currently. His researchinterests are in Nonlinear control, Power systemstability studies, Fuzzy systems and Artificial in-telligence.

Alireza Alfi has received his B.Sc. degree fromFerdowsi University of Mashhad, Mashhad, Iran,in 2000, and his M.Sc. and Ph.D. degrees fromIran University of Technology, Tehran, Iran, in2002 and 2007, all in Electrical Engineering.He joined Shahrood University of Technology in2008, where he is currently an Assistant Profes-sor of Electrical Engineering. His research inter-ests include heuristic optimization, control the-ory, time delay systems, fuzzy logic and chaotic

systems.

Mehdi Siahi recevied the B.Sc. degree in Elecr-tical Engineering from the Yazd University, YazdIRAN in 2001 and M.Sc. degree in Control Engi-neering from the Shahrood University of Thech-nology, Shahrood, Iran, in 2003. He obtained thePh.D. degree in cotrol engineering from shahroodUniverstity of Thechnology, Shahrood, Iran, in2008. He is now an assistant professor and hasbeen with Faculty of Electrical Engineering, Is-lamic Azad University of garmsar Branch, Iranfrom 2004. His current research is on fault Toler-

ant Control systems, Robust Control and Nonlinear systems

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AUTHORS’ ADDRESSESMohammad Hassan khooban, M.Sc.Davood Nazari Maryam Abadi, M.Sc.Asst. Prof. Mehdi Siahi. Ph.D.Department of Electrical and Robotic Engineering,Islamic Azad University of Garmsar Branch, Garmsart,Iran,email: [email protected], [email protected],[email protected]. Prof. Alireza Alfi, Ph.D.Faculty of Electrical and Robotic Engineering,Shahrood University of Technology, Shahrood, Iran,email: [email protected]

Received: 2012-03-18Accepted: 2012-06-21

78 AUTOMATIKA 55(2014) 1, 69–78

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Optimal Type-2 Fuzzy Controller For HVAC Systems

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